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<b>let </b><font color="Maroon" title="c6">w</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D14" target="_self" title="BILINEAR:def.14">BILINEAR:def 14</a><br/>

<b>set </b><font color="Maroon" title="c7">Ffg</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="bilinear.html#K2" title="BILINEAR:func.2">+</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">w</font>;<br/>
<b>set </b><font color="Maroon" title="c8">Ff</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font>;<br/>
<b>set </b><font color="Maroon" title="c9">Fg</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font>;<br/>
<b>let </b><font color="Maroon" title="c10">v</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">W</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a><br/><b>let </b><font color="Maroon" title="c11">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of ;<br/>



<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="bilinear.html#K2" title="BILINEAR:func.2">+</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c10">v</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c10">v</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T14" target="_self" title="BILINEAR:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D6" title="HAHNBAN1:def.6">HAHNBAN1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a></i>
<br/>.= 
<font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D6" title="HAHNBAN1:def.6">HAHNBAN1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c11">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="bilinear.html#K2" title="BILINEAR:func.2">+</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T14" target="_self" title="BILINEAR:th.14">Th14</a></i>
;<br/>


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